Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 513 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.If 6 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹78 (b) ₹432 (c) ₹42 (d) ₹72
2. 2.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 45 days (d) 9 days
3. 3.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 11 days (d) 16 days
4. 4.If 8 pens cost ₹88, how much do 10 pens cost? (a) ₹121 (b) ₹880 (c) ₹90 (d) ₹110
5. 5.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹9 (d) ₹81
6. 6.If 7 mangoes cost ₹105, how much do 4 mangoes cost? (a) ₹60 (b) ₹75 (c) ₹420 (d) ₹102
7. 7.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 11 days (d) 7 days
8. 8.If 7 notebooks cost ₹56, how much do 8 notebooks cost? (a) ₹64 (b) ₹57 (c) ₹448 (d) ₹72
9. 9.₹51 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹17 (b) ₹35 (c) ₹34 (d) ₹51
10. 10.₹140 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹20 (b) ₹70 (c) ₹100 (d) ₹40
11. 11.If 2 notebooks cost ₹8, how much do 3 notebooks cost? (a) ₹9 (b) ₹24 (c) ₹16 (d) ₹12
12. 12.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 11 days (d) 19 days
13. 13.₹294 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹147 (b) ₹294 (c) ₹245 (d) ₹49
14. 14.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹37 (b) ₹148 (c) ₹259 (d) ₹296
15. 15.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 2 days (d) 19 days
16. 16.If 7 pens cost ₹140, how much do 8 pens cost? (a) ₹141 (b) ₹160 (c) ₹1120 (d) ₹180
17. 17.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹35 (d) ₹49
18. 18.If 7 kites cost ₹21, how much do 8 kites cost? (a) ₹22 (b) ₹27 (c) ₹24 (d) ₹168
19. 19.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 22 days (d) 21 days
20. 20.₹144 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹72 (b) ₹54 (c) ₹18 (d) ₹90
21. 21.If 4 kites cost ₹36, how much do 3 kites cost? (a) ₹35 (b) ₹108 (c) ₹27 (d) ₹36
22. 22.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 12 days (d) 3 days
23. 23.If 2 pens cost ₹40, how much do 3 pens cost? (a) ₹120 (b) ₹41 (c) ₹60 (d) ₹80
24. 24.If 3 mangoes cost ₹66, how much do 8 mangoes cost? (a) ₹176 (b) ₹528 (c) ₹198 (d) ₹71
25. 25.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹156 (b) ₹78 (c) ₹117 (d) ₹39
26. 26.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹124 (b) ₹31 (c) ₹155 (d) ₹186
27. 27.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 10 days (d) 11 days
28. 28.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹54 (d) ₹63
29. 29.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹99 (b) ₹77 (c) ₹11 (d) ₹55
30. 30.If 2 notebooks cost ₹36, how much do 12 notebooks cost? (a) ₹46 (b) ₹234 (c) ₹432 (d) ₹216
31. 31.If 3 pens cost ₹42, how much do 6 pens cost? (a) ₹252 (b) ₹98 (c) ₹45 (d) ₹84
32. 32.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 2 days (d) 15 days
33. 33.If 3 kites cost ₹54, how much do 11 kites cost? (a) ₹198 (b) ₹594 (c) ₹62 (d) ₹216
34. 34.If 3 notebooks cost ₹12, how much do 4 notebooks cost? (a) ₹13 (b) ₹16 (c) ₹20 (d) ₹48
35. 35.If 2 notebooks cost ₹14, how much do 12 notebooks cost? (a) ₹168 (b) ₹84 (c) ₹24 (d) ₹91
36. 36.If 8 mangoes cost ₹152, how much do 5 mangoes cost? (a) ₹760 (b) ₹149 (c) ₹95 (d) ₹114
37. 37.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹10 (c) ₹50 (d) ₹55
38. 38.If 3 kites cost ₹30, how much do 12 kites cost? (a) ₹360 (b) ₹120 (c) ₹39 (d) ₹130
39. 39.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 14 days (c) 15 days (d) 8 days
40. 40.₹126 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹98 (b) ₹14 (c) ₹28 (d) ₹63

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